Partial differential equations in image analysis: continuous modeling, discrete processing

Petros Maragos, Muhammad Akmal Butt

Abstract: Most traditional methodologies in digital image processing start with a discrete model which is directly related to the subsequent discrete processing of the image data. We review some examples and focus on some details of an emerging new methodology that starts from some continuous models provided by PDEs and proceeds with discrete processing of the image data via the numerical implementation of these PDEs on some discrete grid. We examine the PDEs modeling multiscale morphological image analysis and the related eikonal PDE of optics. The PDE approach is very promising because it provides many new mathematical models and has connections with the physics of imaging.